lecture 15 - university of michigan · 2019-08-07 · lecture 15 – tuesday 3/12/2013 enzymatic...
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Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms of
chemical reactions and the design of the reactors in which they take place.
Lecture 15
Lecture 15 – Tuesday 3/12/2013
Enzymatic Reactions
Michealis-Menten Kinetics
Lineweaver-Burk Plot
Enzyme Inhibition
Competitive
Uncompetitive
Non-Competitive
2
3
Active Intermediates and PSSH
Review Last Lecture
4
Active Intermediates and PSSH
Review Last Lecture
1.In the PSSH, we set the rate of formation of the active intermediates equal to zero. If the active intermediate A* is involved in m different reactions, we set it to:
2. The azomethane (AZO) decomposition mechanism is
By applying the PSSH to AZO*, we show the rate law, which exhibits first-order dependence with respect to AZO at high AZO concentrations and second-order dependence with respect to AZO at low AZO concentrations.
01
*.*
m
i
iAnetA rr
)('1
)( 2
2 AZOk
AZOkrN
Enzymes
5
Michaelis-Menten Kinetics Enzymes are protein-like substances with catalytic properties.
Enzyme Unease [From Biochemistry, 3/E by Stryer, copywrited 1988 by Lubert Stryer. Used with
permission of W.H. Freeman and Company.]
Enzymes
6
Enzymes provide a pathway for the substrate to
proceed at a faster rate. The substrate, S, reacts
to form a product P.
A given enzyme can only catalyze only one reaction.
Example, Urea is decomposed by the enzyme urease.
E S
Slow S P
Fast
Enzymes - Urease
7
A given enzyme can only catalyze only one reaction. Urea is decomposed by the enzyme urease, as shown below.
UREASECONH2UREASECONHNH 23
OH
222
EPESOH2
SESE 1k
SESE 2k
EPWSE 3k
The corresponding mechanism is:
Enzymes - Michaelis-Menten Kinetics
8
WSEkrP 3
SEWkSEkSEkr SE 3210
Wkk
Sk
EE t
32
11
Wkk
SEkSE
32
1
SEEEt
Enzymes - Michaelis-Menten Kinetics
9
SK
SEk
Sk
Wkk
SEWkWSEkr
M
V
tcat
K
t
k
P
M
cat
max
1
32
33
SK
SVWSEkr
m
P
max3
Enzymes - Michaelis-Menten Kinetics
10
Turnover Number: kcat
Number of substrate molecules (moles) converted to
product in a given time (s) on a single enzyme molecule
(molecules/molecule/time)
For the reaction:
40,000,000 molecules of H2O2 converted to product per
second on a single enzyme molecule.
H2O2 + E →H2O + O + E kcat
Vmax
=kcat
Et
Enzymes - Michaelis-Menten Kinetics
11
(Michaelis-Menten plot)
Solving:
KM=S1/2
therefore KM is the
concentration at which the rate
is half the maximum rate.
Vmax
-rs
S1/2 CS
Michaelis-Menten Equation
SK
SVrr
M
maxSP
2/1M
2/1maxmax
SK
SV
2
V
Enzymes - Michaelis-Menten Kinetics
12
S
1
V
K
V
1
r
1
max
M
maxS
Inverting yields:
Lineweaver-Burk Plot
slope = KM/Vmax
1/Vmax
1/S
1/-rS
Types of Enzyme Inhibition
13
)inactive( EIIE
Competitive
)inactive( SEIISE
Uncompetitive
)inactive( SEIISE
)inactive( SEISEI
Non-competitive
Competitive Inhibition
14
Competitive Inhibition
15
2
31
k
kk
PESESE
SE3P Ckr
IEIE
IEIE EPSE
SESE SESE
1) Mechanisms:
5
4
k
k
)inactive(IEI E
2) Rate Laws:
SE3SE2ES1SE CkCkCCk0r
4
5I
I
EIEI
k
kK
K
CCC
m
ES
32
ES1SE
K
CC
kk
CCkC
m
ES3P
K
CCkr
EI5EI4EI CkCCk0r
16
Competitive Inhibition
17
Competitive Inhibition
I
I
m
S
EtotEEISEEEtot
K
C
K
C1
CC CCCC
SI
I
max
m
maxS C
1
K
C1
V
k
V
1
r
1
I
mISm
SEtot3P
K
KCCK
CCkr
I
ImS
SmaxS
K
C1KC
CVr
18
Competitive Inhibition From before (no competition):
S
M
S CV
K
Vr
111
maxmax
Intercept does not change, slope increases as
inhibitor concentration increases
max
slopeV
KM
max
1Intercept
V
Sr
1
SC
1
No Inhibition
Competitive
Increasing CI
Competitive
SI
IM
S CK
C
V
K
Vr
11
11
maxmax
Uncompetitive Inhibition
19
Uncompetitive Inhibition
20
PSESE 3
2
1
k
k
k
SEkrr catSP
Inhibition only has affinity for enzyme-substrate complex
Developing the rate law:
SEIkSEIkSEkSEkSEkr catSE 54210 (1)
0r SEI SEIkSEIk 54 (2)
)inactive(SEISEI
5
4
k
k
Adding (1) and (2)
Mcat
cat
K
SE
kk
SEkSE
SEkSEkSEk
2
1
21 0
M
catcatp
I
MII
K
SEkSEkr
k
kK
KK
SEI
K
SEISEI
k
kSEI
4
5
5
4
From (2)
21
Uncompetitive Inhibition
MIM
M
tcatp
MIM
t
KK
SI
K
SK
SEkr
KK
SI
K
SE
SEISEEE
1
1
Total enzyme
I
M
PS
K
ISK
SVrr
1
max
22
Uncompetitive Inhibition
Slope remains the
same but intercept
changes as inhibitor
concentration is
increased
Lineweaver-Burk Plot for uncompetitive inhibition 23
I
M
S
I
M
S
K
I
VSV
K
r
K
ISK
SVr
1111
111
maxmax
max
Uncompetitive Inhibition
Non-competitive Inhibition
24
Non-competitive Inhibition
25
Both slope and intercept
changes
SC
1
Sr
1
Increasing I
No Inhibition
E + S E·S P + E
(inactive)I.E + S I.E.S (inactive)
+I +I -I -I
I
I
S
M
I
I
S
I
ISM
SS
k
C
CV
k
k
C
Vr
k
CCk
CVr
11
111
1
maxmax
max
26
Summary: Types of Enzyme Inhibition
Lineweaver–Burk plots for three types of enzyme inhibition.
27
End of Lecture 15
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